Conversion of electrical power from an input AC form to an output AC form is used extensively in industrial applications. In particular, three-phase bi-directional AC/DC/AC converters have been employed in motor drive applications, power generation systems, line conditioners and uninterruptible power supply systems (UPS). This type of converter provides sinusoidal current and adjustable power factor in both the input (line) side and the output (load) side. Conventional three-phase bi-directional AC/DC/AC converters include two three-phase PWM inverters coupled to a dc-link that provides some form of reactance, such as a capacitor or inductor for back-to-back voltage or current source configurations, respectively. This type of conversion system is sometimes referred to as a two-stage converter since the conversion occurs in two stages, the first involving conversion from three-phase AC to DC, and the second providing conversion from DC to three-phase output AC, where the output AC can have variable voltage and/or frequency. However, because there are two energy conversions, the energy efficiency of conventional two-stage converters is lower than single-stage conversions. Direct AC-to-AC converters have been proposed to address this efficiency, including AC/AC matrix converters, in which the energy in three-phase input AC voltage is directly transferred to the three-phase output voltage. However, three-phase AC/AC matrix converters require 18 power switching devices as well as complicated commutation switching controls with snubber circuits to avoid input side short circuit and output side open-circuit conditions. So-called sparse matrix converters have also been introduced in an attempt to decrease the number of switching devices. These converters essentially modify the standard matrix converter by the use of two-stage energy conversion from AC to DC and then from DC to AC. The sparse matrix converters do not require DC link reactance components, and switch loss of input side switches can be reduced by special PWM switching control. However, the sparse matrix converter designs require three additional switching devices and six extra diodes compared with 12 power switching devices used in standard two-stage AC/DC/AC converters. Thus, there is a continuing need for improved conversion system designs by which one form of AC electrical power can be efficiently converted to a second AC form without requiring a large number of switching devices or complicated switching controls.